Stephen Sackur listens in to private telephone calls made from the Oval Office for an insight into the minds of Presidents John F Kennedy, Lyndon B Johnson and Richard Nixon, who all insisted on taping their conversations.

In the summer of 1962, President Kennedy decided to make clandestine recordings of some of his telephone calls from the Oval Office.

The "on" button for his tape machine was ingeniously hidden in a pen-holder on the presidential desk.

Kennedy controlled his secret tape machine from his desk

For the next 11 years, through the presidencies of Kennedy, Johnson and Nixon, the covert recording continued. The result? An insight into the minds of three men wielding extraordinary power in a turbulent decade.

Had it not been for the Watergate scandal, and the exposure of Richard Nixon's incriminating tapes, this gold mine of intimate archive material might have remained undiscovered.

Thankfully in the post-Watergate era the archives were opened up. Neither before nor since have we been afforded such a penetrating glimpse into the realities of "the most powerful job in the world".

Kennedy was the most sparing of the three in his use of the tape recorder.

He never explained why he started making the tapes - maybe it was vanity, maybe part of a plan to write his memoirs later in life - but there was almost certainly a harder edge to his reasoning.

He appears to have viewed his record of sensitive conversations with staff, political allies and enemies as a powerful tool. A means of persuasion, sometimes coercion.

Cuban missile crisis

The most gripping episode in the Kennedy archive spans those tension-filled days of late October 1962 when it seemed that the world was teetering on the brink of nuclear war.

The cause was Cuba, specifically the Soviet decision to install long-range missiles on the Communist island.

JFK was just 45-years-old at the time of the missile crisis. Khrushchev believed he could outsmart this untested, callow president.

But on tape we hear a different Kennedy: amazingly relaxed at the height of the stand-off, aware of the terribly high stakes but undaunted.

As presidents so often do, he called a predecessor (in this case Eisenhower) to discuss the options:

JFK: General, what if Khrushchev announces tomorrow, which I think he will, that if we attack Cuba it's going to be nuclear war? And what's your judgement as to the chances they'll fire these things off if we invade Cuba?

Eisenhower: Oh, I don't believe they will... something may make these people shoot them off. I just don't believe they will.

JFK: (Chuckles) Yeah well, we'll hang on tight...

Kennedy did hang on tight. And the Soviets withdrew their missiles. It was a masterful piece of crisis management, but within a year JFK was dead.

His successor in the White House, Lyndon Baines Johnson, is in some ways the star turn of these secret tapes. He was Texan through and through.

LBJ: "I'm relying on you, Jackie"

A politician who could charm and bully with equal force, his charisma was matched by his vulgarity.

Unlike Kennedy, Johnson wasn't always disciplined with his recording equipment - he often forgot to turn it off during intensely personal conversations.

Perhaps the most memorable of his calls was to Jackie Kennedy soon after the assassination.

He reaches out to Jackie for both political and personal reasons:

LBJ: You've got this president relying on you. And this isn't the first one you've had! There's not many women running around with a good many presidents. So you just bear that in mind. You've got the biggest job of your life!

Jackie: "She ran around with two presidents" - that's what they'll say about me!

Johnson took on the white segregationists and won some crucial battles. He took on the Vietnamese communists and made some disastrous mistakes. But through it all the tapes give you a sense of his rough-hewn charm.

He called his tailor down in Dallas to order a new pair of trousers:

LBJ: The crotch down where your nuts hang - it's always a little too tight. It's like riding a wire fence. See if you can't give me an inch where the zipper ends, right back to my bunghole. (The president then lets out a magnificent belch.)

Nixon's secret recordings proved to be his undoing

Richard Nixon is the president who will forever be associated with "secret tapes". "Tricky Dickie" had a sophisticated voice-activated recording system installed in the White House in 1971. But it proved to be a weapon of personal destruction.

Nixon's paranoia, his chippiness and self-pity are evident in many of his recordings.

This is just one example from a discussion he had with his Attorney General, John Mitchell, about a potential nominee to the Supreme Court:

RN: I didn't go to a number one law school, John... this number one law school bullshit is getting me down a little, isn't it you?

JM: It has for about 30 years

RN: Well, sure - you've seen a lot of Harvard men around, they're soft in the head. And they don't work as hard...

It's a remarkable and salutary experience - to eavesdrop on American presidents.

By dint of their position they are the world's most powerful human beings, but they are not supermen. They have flaws and foibles like the rest of us. They show wisdom and sometimes they get things terribly wrong.

Kennedy, Johnson and Nixon; each made more tapes than the last; all wanted a private record of their work in the White House, but none of them ever dreamed we would listen in.

This is the White House Calling is broadcast on BBC Radio 4 at 2000 BST on 25 October.